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Title: An Easy Method To Accelerate An Iterative Algebraic Equation Solver

This article proposes to add a simple term to an iterative algebraic equation solver with an order n convergence rate, and to raise the order of convergence to (2n - 1). In particular, a simple algebraic equation solver with the 5th order convergence but uses only 4 function values in each iteration, is described in details. When this scheme is applied to a Newton-Raphson method of the quadratic convergence for a system of algebraic equations, a cubic convergence can be achieved with an low overhead cost of function evaluation that can be ignored as the size of the system increases.
Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
1116976
Report Number(s):
LLNL-TR--648574
DOE Contract Number:
W-7405-ENG-48; AC52-07NA27344
Resource Type:
Technical Report
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE